Zobrazeno 1 - 10
of 19
pro vyhledávání: '"Jaoui, Remi"'
Autor:
Jaoui, Remi
Two theorems witnessing the abundance of geometrically trivial strongly minimal autonomous differential equations of arbitrary order are shown. The first one states that a generic algebraic vector field of degree $d\geq 2$ on the affine space of dime
Externí odkaz:
http://arxiv.org/abs/2301.06362
Autor:
Jaoui, Rémi, Moosa, Rahim
A new tool for the model theory of differentially closed fields and of compact complex manifolds is here developed. In such settings, it is shown that a type internal to the field of constants (resp. to the projective line) admits a maximal image who
Externí odkaz:
http://arxiv.org/abs/2207.07515
It is shown that if $p$ is a complete type of Lascar rank at least 2 over $A$, in the theory of differentially closed fields of characteristic zero, then there exists a pair of realisations, $a_1$ and $a_2$, such that $p$ has a nonalgebraic forking e
Externí odkaz:
http://arxiv.org/abs/2206.13450
We study the structure of the solution sets in universal differential fields of certain differential equations of order two, the Poizat equations, which are particular cases of Li\'enard equations. We give a necessary and sufficient condition for str
Externí odkaz:
http://arxiv.org/abs/2201.03838
Given an algebraic differential equation of order greater than one, it is shown that if there is any nontrivial algebraic relation amongst any number of distinct nonalgebraic solutions, along with their derivatives, then there is already such a relat
Externí odkaz:
http://arxiv.org/abs/2110.08123
We first elaborate on the theory of relative internality in stable theories, focusing on the notion of uniform relative internality (called collapse of the groupoid in an earlier work of the second author), and relating it to orthogonality, trivialit
Externí odkaz:
http://arxiv.org/abs/2009.06014
Autor:
Jaoui, Rémi
Publikováno v:
Alg. Number Th. 15 (2021) 2449-2483
In this article, we study model-theoretic properties of algebraic differential equations of order $2$, defined over constant differential fields. In particular, we show that the set of solutions of a general differential equation of order $2$ and of
Externí odkaz:
http://arxiv.org/abs/1905.09429
Publikováno v:
In Advances in Mathematics 15 February 2023 415
Autor:
Jaoui, Rémi
In this article, we develop a geometric framework to study the notion of semi-minimality for the generic type of a smooth autonomous differential equation $(X,v)$, based on the study of rational factors of $(X,v)$ and of algebraic foliations on $X$,
Externí odkaz:
http://arxiv.org/abs/1803.08811
Autor:
Jaoui, Remi
We define the notion of a smooth pseudo-Riemannian algebraic variety $(X,g)$ over a field $k$ of characteristic $0$, which is an algebraic analogue of the notion of Riemannian manifold and we study, from a model-theoretic perspective, the algebraic d
Externí odkaz:
http://arxiv.org/abs/1703.02890